Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds

Details Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds

2005-08-21

arxiv.org/abs/math/0508389v1

Mathematics

Differential Geometry

17 pages. to appear in CVPDE

Scientific paper

In this note we study the conformal metrics of constant $Q$ curvature on
closed locally conformally flat manifolds. We prove that for a closed locally
conformally flat manifold of dimension $n\geq 5$ and with Poincar\"{e} exponent
less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$
and positive scalar curvature is compact in the $C^\infty$ topology.

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